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Modal stability analysis provides information about the long-time growth or decay of small-amplitude perturbations around a steady-state solution of a dynamical system. In fluid flows, exponentially growing perturbations can initiate departure from laminar flow and trigger transition to turbulence. Although flow of a Newtonian fluid through a pipe is linearly stable for very large values of the Reynolds number ($Re sim 10^7$), a transition to turbulence often occurs for $Re$ as low as $1500$. When a dilute polymer solution is used in the place of a Newtonian fluid, the transitional value of the Reynolds number decreases even further. Using the spectral collocation method and Oldroyd-B constitutive equation, Garg et al. (Phys. Rev. Lett. 121:024502, 2018) claimed that such a transition in viscoelastic fluids is related to linear instability. Since differential matrices in the collocation method become ill-conditioned when a large number of basis functions is used, we revisit this problem using the well-conditioned spectral integration method. We show modal stability of viscoelastic pipe flow for a broad range of fluid elasticities and polymer concentrations, including cases considered by Garg et al. Similarly, we find that plane Poiseuille flow is linearly stable for cases where Garg et al. report instability. In both channel and pipe flows, we establish the existence of spurious modes that diverge slowly with finer discretization and demonstrate that these can be mistaken for grid-independent modes if the discretization is not fine enough.
Modal and nonmodal analyses of fluid flows provide fundamental insight into the early stages of transition to turbulence. Eigenvalues of the dynamical generator govern temporal growth or decay of individual modes, while singular values of the frequen
Newtonian pipe flow is known to be linearly stable at all Reynolds numbers. We report, for the first time, a linear instability of pressure driven pipe flow of a viscoelastic fluid, obeying the Oldroyd-B constitutive equation commonly used to model d
The flow of viscoelastic fluids in channels and pipes remain poorly understood, particularly at low Reynolds numbers. Here, we investigate the flow of polymeric solutions in straight channels using pressure measurements and particle tracking. The law
Common modal decomposition techniques for flowfield analysis, data-driven modeling and flow control, such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are usually performed in an Eulerian (fixed) frame of reference wi
In this numerical study, an original approach to simulate non-isothermal viscoelastic fluid flows at high Weissenberg numbers is presented. Stable computations over a wide range of Weissenberg numbers are assured by using the root conformation approa